6 problems

da Silva Machado–Seade conjecture. Weighted homogeneity of $(D,0)$ is characterized by the existence of a holomorphic vector field tangent to $D$ and transverse to all sufficiently…

Machado–Seade conjecture. The following statements are equivalent: $(D,0)$ is weighted homogeneous; there exists a holomorphic vector field tangent to $D$ with an isolated singular…

Let $m,i\in\mathbb{Z}_{\geq 0}$, and let $\widetilde{f_i^m}(x,y)$ be the deformed polynomial defined from the coefficients of … For a polynomial $g$, write $g\in((x+y+m)_{2m+1})$ w…

Terao-type conjecture. The invariant $\nu(C)$ is combinatorially determined.

Let $C$ be an irreducible nodal plane curve of degree $d$, with $d\geq 4$. A curve is Torelli if it is determined by its associated logarithmic vector bundle $T\langle C\rangle$. G…

Let $C$ be an irreducible nodal plane curve, and call $C$ Torelli if it is determined by its associated logarithmic vector bundle $T\langle C\rangle$ up to the relevant equivalence…